Rectangle QRST has coordinates Q ( − 3 , 7 ) , R ( − 3 , 11 ) , S ( 4 , 11 ) , and T ( 4 , 7 ) . Dilate the rectangle by a scale factor of 3 with a center of dilation at the origin. What are the coordinates of rectangle Q 'R 'S 'T '? Explain your reasoning. Q ' ( , ) R ' ( , ) S ' ( , ) T ' ( , ) Is the dilation a reduction or an enlargement? Explain your reasoning.

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musiclover10045 musiclover10045 · Answer 1 · 2019-10-07T17:43:05+02:00

Because the scale factor is at the origin, you multiply all the coordinates by the scale factor:

Q(-3,7) = Q'(-3*3, 7*3) = Q'(-9,21)

R(-3,11) = R(-3*3, 11*3) = R'(-9,33)

S(4,11) = S'(4*3,11*3) = R'(12,33)

T(4,7) = T'(4*3, 7*3) = T'(12,21)

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JeanaShupp JeanaShupp · Answer 2 · 2019-10-23T09:33:27+02:00

Answer: Q'(-9,21), R'(-9,33), S'(12,33) and T'(12,21)

It is enlargement.

Step-by-step explanation:

Given : Rectangle QRST has coordinates Q (− 3 , 7 ) , R (− 3 , 11 ) , S ( 4 , 11 ) , and T ( 4 , 7 ) .

Scale factor =3 >1 , so it is an enlargement. [Figure enlarge using scale factor greater than 1 ]

The rule we use for dilating a figure using center of dilation at the origin and scale factor k:

[tex](x,y)\to (kx, ky)[/tex]

Then, the coordinates of rectangle Q 'R 'S 'T ' will be :-

[tex]Q(-3,7)\to Q'(\ 3(-3)\ ,\ 3(7)\ )=Q'(-9,21)[/tex]

[tex]R(-3,11)\to R'(\ 3(-3)\ ,\ 3(11)\ )=R'(-9,33)[/tex]

[tex]S(4,11)\to S'(\ 3(4)\ ,\ 3(11)\ )=S'(12,33)[/tex]

[tex]T(4,7)\to T'(\ 3(4)\ ,\ 3(7)\ )=T'(12,21)[/tex]

Hence, the coordinates of rectangle Q 'R 'S 'T ' are : Q'(-9,21), R'(-9,33), S'(12,33) and T'(12,21)